Renshaw Cell Recurrent Inhibition Improves Physiological Tremor by Reducing Corticomuscular Coupling at 10 Hz

6616 • The Journal of Neuroscience, May 20, 2009 • 29(20):6616–6624

Behavioral/Systems/Cognitive Renshaw Cell Recurrent Inhibition Improves Physiological Tremor by Reducing Corticomuscular Coupling at 10 Hz

Elizabeth R. Williams and Stuart N. Baker Institute of Neuroscience, Newcastle University, Newcastle upon Tyne NE2 4HH, United Kingdom

Corticomuscular coherence between the primary motor cortex (M1) and hand muscle electromyograms (EMG) occurs at ϳ20 Hz but is rarely seen at ϳ10 Hz. This is unexpected, because M1 has oscillations at both frequencies, which are effectively transmitted to the spinal cord via the corticospinal tract. We have previously speculated that a specific “neural filter” may selectively reduce coherence at ϳ10 Hz. This would have functional utility in minimizing physiological tremor, which often has a dominant component around this frequency. Recurrent inhibition via Renshaw cells in the spinal cord is a putative neural substrate for such a filter. Here we investigate this system in more detail with a biophysically based computational model. Renshaw cell recurrent inhibition reduced EMG oscillations at ϳ10 Hz, and also reduced corticomuscular coherence at this frequency (from 0.038 to 0.014). Renshaw cell inhibitory feedback also generated synchronous oscillations in the motoneuron pool at ϳ30 Hz. We show that the effects at 10 Hz and 30 Hz can both be understood from the dynamics of the inhibitory feedback loop. We conclude that recurrent inhibition certainly plays an important role in reducing 10 Hz oscillations in muscle, thereby decreasing tremor amplitude. However, our quantitative results suggest it is unlikely to be the only system for tremor reduction, and probably acts in concert with other neural circuits which remain to be elucidated.

Introduction gested as a mechanism for tremor reduction by preventing exces- All of us experience the involuntary shaking of the hands which is sive motoneuron synchronization (Stein and Oguztoreli, 1984; physiological tremor. This tremor places severe constraints on Windhorst, 1996; Matthews, 1997), or alternatively as the gener- ϳ motor performance. Individuals with exceptionally precise mo- ator of 10 Hz physiological tremor (Elble and Randall, 1976). A tor control, such as champion dart players and microsurgeons, previous modeling study showed that recurrent inhibition re- have very low tremor; drugs which artificially reduce tremor are duces motoneuron correlations (Maltenfort et al., 1998). banned in many sports. Although many factors contribute to In this study, we report results from a biophysically based tremorigenesis, an important component comes from neural os- computational model designed to investigate the effects of recur- cillators rhythmically active at ϳ10 Hz (Elble and Koller, 1990). rent inhibition on corticomuscular coherence. We show that the During a sustained contraction, primary motor cortex (M1) known dynamics of the Renshaw cell feedback loop lead to partial shows oscillations at both ϳ10 Hz and ϳ20 Hz (Murthy and Fetz, cancellation of oscillations around 10 Hz, thereby markedly re- 1992; Conway et al., 1995; Halliday et al., 1998). Both these fre- ducing corticomuscular coherence and tremor amplitude. quency ranges are effectively carried down the corticospinal tract (Baker et al., 2003), which in old-world primates including man Materials and Methods makes direct monosynaptic connections to motoneurons (Porter Overview of model. The model builds on our previously published work and Lemon, 1993). However, the majority of studies find that (Baker and Lemon, 1998; Williams and Baker, 2009). It consists of a pool only ϳ20 Hz oscillations are coherent between M1 and hand of realistic motoneurons, which receive common input from the motor muscles (Conway et al., 1995; Baker et al., 1997, 2003; Salenius et cortex (Fig. 1A). EMG and Force are simulated from the firing of the al., 1997; Halliday et al., 1998; Kilner et al., 2000). Based on these motoneurons. Renshaw cell spinal interneurons provide recurrent inhi- puzzling observations, we have previously speculated that a neu- bition to the motoneurons. The model produces output signals corre- ral system may actively filter out ϳ10 Hz oscillations in motoneu- sponding to those which would be measured experimentally, which can ron firing (Baker et al., 2003). This would be advantageous in be used in a coherence calculation. Motoneuron model. The motoneuron model was based on a previously minimizing physiological tremor. published model (Booth et al., 1997). It includes a somatic and dendritic Renshaw cells receive excitatory input from motoneurons, compartment, and eight active conductances found in mammalian mo- and feed back inhibition to the same motoneuron pool (Ren- toneurons (soma, gNa, gK(DR), gCa-N, gK(Ca),gNa-P; dendrite, gCa-L, gCa-N, shaw, 1941). This recurrent inhibition has been variously sug- gK(Ca)) each with Hodgkin–Huxley style kinetics. The values of gK(Ca) were 3.136 and 0.69 mS/cm 2 for the somatic and dendritic compart- ments respectively. We added a sodium persistent inward current (PIC) Received Jan. 17, 2009; revised March 25, 2009; accepted March 27, 2009. This work was funded by the Wellcome Trust and the Medical Research Council (studentship to E.R.W.). in the soma with kinetics chosen to fit data from Li and Bennett (2003). Correspondence should be addressed to Prof. Stuart N. Baker, Institute of Neuroscience, Newcastle University, This conductance shows strong clamp control in both voltage and cur- Henry Wellcome Building, Newcastle upon Tyne NE2 4HH, UK. E-mail: [email protected]. rent clamp experiments, suggesting that the responsible channels are DOI:10.1523/JNEUROSCI.0272-09.2009 primarily located on or near the soma (Lee and Heckman, 2001). Copyright © 2009 Society for Neuroscience 0270-6474/09/296616-09$15.00/0 Each motoneuron received excitatory common input from a cortical Williams and Baker • Renshaw Cells Improve Tremor J. Neurosci., May 20, 2009 • 29(20):6616–6624 • 6617

duce the total synaptic conductance ( gt-syn) in the dendrite. The reversal potential for the synaptic conductance was set to 0 mV (Baker ␶ and Lemon, 1998). The values of and gmax were chosen to produce an EPSP in the somatic compartment with a rise time of 1 ms and a peak of 100 ␮V (Asanuma et al., 1979). The properties of motoneurons vary con- tinuously across the motoneuron pool, such that units generating the smallest twitch tension are recruited first (Zajac and Faden, 1985). An orderly variation in motoneuron membrane properties underlies this (Bakels and Kernell, 1993). In this model, orderly recruitment was simulated by changing the ra- tio of soma surface area to total surface area. The parameter P in the model of Booth et al. (1997) determines the proportion of the dendrite membrane potential allowed to activate the motoneuron. The value of P used in each motoneuron was adjusted to vary the firing rate with recruitment number. The first motoneuron to be recruited (MN1) was assigned ϭ P1 0.1. Simulations were then run of this motoneuron model in receipt of different levels of total synaptic input; this allowed the construction of a curve of output firing rate versus synaptic input rate (Fig. 1C). The model of Wani and Guha (1975) was used to determine the firing rate of the first motoneuron when the jth is just recruited. The strength of total synaptic input needed to make MN1 fire at this rate was then deter-

mined from the input-output curve. Pj was then adjusted until the jth motoneuron fired at the minimum recruitment-firing rate with this level of input. The procedure was re- peated for all motoneurons; this resulted in estimates of P which increased exponentially with recruitment number. Adjusting P in this way does not accurately reflect the processes which determine recruitment order in real motoneurons, but was a convenient means to Figure 1. A, Schematic of the model. B, Example raw data output from model. C, Cross-correlation between Renshaw cell and match the rates across the pool to those pre- motoneuron spikes, averaged over all possible pairs. dicted by Wani and Guha’s (1975) model. In the resulting motoneuron pool, the afterhy- source. The number of inputs arriving per 0.2 ms time step was modeled perpolarization (AHP) varied in amplitude as white Gaussian noise with both mean and variance equal to 0.5. This is from 7.2 to 9.1 mV below threshold. The time taken for the AHP to equivalent to each motoneuron receiving 2500 impulses/s which is con- reach half maximum ranged from 17.2 ms to 18.1 ms. These decay sistent with published reports (Fritz et al., 1985; Porter and Lemon, 1993; times correspond with exponential time constants of 24–26 ms, in Baker et al., 2001; Davies et al., 2006). In some simulations, the cortical keeping with previous models of motoneurons (Matthews, 1997). input was modeled as colored Gaussian noise, with peaks at 8–12 Hz and Our simulations of motoneurons had a coefficient of variation (CV) of 18–30 Hz, to simulate the cortical oscillations seen experimentally (Con- the interspike intervals between 9 and 10%. This corresponds to the way et al., 1995; Kilner et al., 2000). lower end of the range found experimentally (10–30%) (Moritz et al., Each motoneuron also received an independent input (white Gaussian 2005). For the simulations which omitted PICs, the CVs were slightly noise), which was independent both from the common input and also higher, at 11–13%. from the independent input to all other motoneurons. The mean and variance were adjusted with reference to preliminary simulations to pro- Motor units. The motoneuron pool comprised 377 neurons (Wani and duce a force output at the desired percentage of maximal voluntary con- Guha, 1975; Baker and Lemon, 1998). After the firing of each motoneu- traction (MVC). This required that the independent input had a mean ron, a peripheral motor unit produced a motor unit action potential 3.2 times larger than the cortical input. (MUAP) and twitch tension. The peripheral conduction delay for the jth The time course of synaptic conductances was modeled as an ␣-func- motoneuron was given by (11 ϩ 2j/377) ms; this accounts for the slightly tion: faster conduction velocity of the higher threshold motoneurons (Baker and Lemon, 1998). MUAPs were as used as in our previous publication t t ϭ ⅐ ͩ Ϫ ͪ (Baker and Lemon, 1998); these are designed realistically to reflect the gsyn gmax ␶ exp 1 ␶ , (1) MUAPs which would be measured from a human hand muscle using ␶ ␣ where gmax is the maximum conductance and is the rise time (Baker surface recordings. Twitch tensions were simulated as functions (sim- and Lemon, 1998). Unitary synaptic conductances summed to pro- ilar to Eq. 1); the rise time and amplitudes varied across the pool as 6618 • J. Neurosci., May 20, 2009 • 29(20):6616–6624 Williams and Baker • Renshaw Cells Improve Tremor specified for the first dorsal interosseous muscle by the model of (Wani Model simulation. The model was implemented in the MATLAB envi- and Guha, 1975). ronment (MathWorks), using the MATLAB Distributed Computing EMG was simulated by linear summation of the MUAPs from all active Toolbox and Engine to run multiple simulations simultaneously on a motor units. In contrast, the summation of single twitch tensions to 16-processor computer cluster. Differential equations governing generate total output force has been demonstrated to have several non- motoneuron membrane potential were solved using the exponential in- linearities. Twitches summate more effectively at low spike rates, gener- tegration scheme (MacGregor, 1987), with a time step of 0.2 ms. ating a sigmoidal dependence between rate and force (Rack and West- Analysis. All analysis proceeded along similar lines to that normally bury, 1969). Fuglevand et al. (1993) developed a model to incorporate used for experimental data. Simulated EMGs were full wave rectified. these nonlinearities in force production, which was used here. Signals were split into 0.8192-s-long (4096 sample points) disjoint seg- Renshaw cells. Sixty-four Renshaw cells (RCs) were simulated with a ments before calculating power spectra, coherence and coherence phase model similar to that of Maltenfort et al. (1998), and used a point neuron using formulae given in full in Baker et al. (2006). Coherence measures model following MacGregor (1987). The membrane time constant was the correlation between two signals in the frequency domain, and is 8.0 ms, and the values of parameters B and tGK (the peak conductance bounded by 0 and 1. The coherence between two signals, x and y, was and time constant of the potassium conductance respectively) were ad- calculated according to the following: justed to match experimental data from Hultborn and Pierrot- 2 Deseilligny (1979) on the after-hyperpolarization (AHP) and steady state L ͯ͸ ͑ ͒ *͑ ͒ͯ rate/current relationship. The resulting AHP had a duration of 36 ms and Xi f Yi f a peak of 2.3 mV, similar to experimental data (Hultborn and Pierrot- iϭ1 Coh͑ f ͒ ϭ , (3) Deseilligny, 1979; Hultborn et al., 1979). Synaptic inputs from motoneu- L L rons to the RCs were modeled as an ␣ function time course, producing ͸X ͑ f ͒X* ͸Y ͑ f ͒Y*͑ f ͒ EPSPs with 7.6 ms rise time, 50 ms duration and 0.6 mV peak (Walmsley i i i i iϭ1 iϭ1 and Tracey, 1981). Renshaw cells received a source of synaptic input, which was independent of the motoneuron firing, and independent for where X and Y are the Fourier transforms of the signals, f is the frequency, each cell. The number of inputs per time step was determined by white and L is the number of disjoint segments averaged over. The 95% signif- Gaussian noise, with a mean and variance of 2.27 inputs per 0.2 ms time icance limit was determined by the following: step, yielding a background firing rate of 11 Hz. This simulated the known supraspinal input to Renshaw cells which is independent from the 1 Ϫ ͑1 Ϫ 0.05͒1/͑LϪ1͒ . (4) motoneurons (Windhorst, 1996). Distribution of recurrent inhibition was uniform and independent of Power spectra were normalized as described by Witham and Baker motoneuron type in the model. This is not physiologically realistic be- (2007). The coherence phase was determined by the following: cause there is evidence that recurrent inhibition has a limited spatial extent (McCurdy and Hamm, 1994), and that the strength of recurrent L ␪ ͑ f ͒ ϭ arg ͩ͸X ͑ f ͒Y*͑ f ͒ͪ . inhibition may depend on motoneuron recruitment number (Hultborn i i et al., 1988a,b). However, since we are simulating such a low force (5% iϭ1 MVC), with a correspondingly limited number of active motoneurons, The 95% confidence limits on phase were estimated according to the this simplification is unlikely materially to affect our results on the tem- following (Rosenberg et al., 1989): poral dynamics of the inhibition. The number of Renshaw cells contacting each MN varied from 10 to 20; the number of MNs contacting each 1 1 1/ 2 Renshaw cell varied from 20 to 50. These values represent a realistic level ␪ ͑ ͒ Ϯ ͫ ͩ Ϫ ͪͬ f 1.96 ͉ ͑ ͉͒2 1 . (6) of connectivity given existing experimental data (Van Keulen, 1981; L coh f Hamm et al., 1987; Alvarez et al., 1999).A1msconduction delay was introduced for both motoneuron to Renshaw cell, and Renshaw cell to motoneuron contacts. Renshaw cells produced a unitary IPSP in MNs at Results resting potential with an amplitude of 46.2 ␮V, rise time of 5.5 ms and Impact of Renshaw cell recurrent inhibition half-width of 18.5 ms, comparable to experimental data (Hamm et al., Figure 2 shows corticomuscular coherence spectra calculated 1987). The Renshaw cell synapses contacted the motoneuron dendritic from simulations of our model. When no Renshaw cells were compartment, consistent with published data (Fyffe, 1991). included (black line) the coherence was significant between 2 and To estimate the gain (G) of the recurrent feedback loop, we first mea- 70 Hz, with distinct peaks at ϳ10, ϳ20, ϳ30, and ϳ40 Hz. The sured the total firing rate (A ) across the whole motoneuron pool for a 0 appearance of these peaks reflects the nonlinear properties of the simulation without Renshaw cells. In simulations with Renshaw cells, the motoneuron pool. At the contraction strength simulated (5% independent input to motoneurons was usually increased to counteract the inhibition of the motoneurons, and to maintain the same firing rate. MVC), all active motoneurons fire around 10 Hz. The common However, to estimate the gain G, we ran a simulation without Renshaw input synchronizes the motoneurons. Because the motoneuron cells, but with this higher level of independent input. The increased total firing rates are concentrated around 10 Hz, this frequency and its motoneuron firing rate A1 was then measured from this simulation. Gain harmonics appear strongly in the corticomuscular coherence was then calculated as follows: spectrum – even though the common input was simulated as white noise. At the weak contraction strengths which we com- A1 monly use for fine motor control, a motoneuron pool thus has a G ϭ Ϫ 1 . (2) A0 worrying propensity to generate and accentuate ϳ10 Hz physiological tremor. ϭ We found G 0.12; this is similar to the values of loop gain reported The introduction of recurrent inhibition to the model (Fig. 2, in previous simulations by (Maltenfort et al., 1998). red line) reduced corticomuscular coherence at ϳ10 Hz and ϳ20 Figure 1B shows example raw data produced by the model, and includes Hz, but increased it at ϳ30 Hz and ϳ40 Hz. It is tempting to examples of the common cortical input, motoneuron and Renshaw cell membrane potentials, EMG and force for a period of 1 s. interpret this result because an action of the recurrent feedback Figure 1C shows the cross-correlation between Renshaw cells spikes loop. However, there is one possible confounding factor. The and motoneuron spikes, averaged over all possible pairs. There was a simulations with and without Renshaw cells were run at a force clear dip in the cross-correlation at 12 ms, showing that Renshaw cell output of 5% MVC. The addition of inhibitory inputs to the firing inhibited the motoneuron pool. motoneurons in the latter required a higher level of independent Williams and Baker • Renshaw Cells Improve Tremor J. Neurosci., May 20, 2009 • 29(20):6616–6624 • 6619

of the decrease in coherence at 10 Hz, and the rises at 30–40 Hz, must be attributed to the closed-loop inhibitory feedback pro- vided by the Renshaw cell circuit. Figure 2B shows the power spectrum of the force output of the model. The slow time course of motor unit twitch tensions act as a low pass filter, so that this spectrum, approximately equivalent to the overt tremor, was dominated by the ϳ10 Hz peak. Recur- rent inhibition reduced the tremor peak, which would render movements smoother and more precise. The way in which Renshaw cell inhibition has this effect on corticomuscular coherence and tremor can be understood by the further analysis of motoneuron and Renshaw cell spiking shown in Figure 3. In this figure, the red and black lines correspond to simulations with and without Renshaw cells respectively. The autocorrelation histogram averaged over all motoneurons showed a strong 10 Hz periodicity, reflecting the cells’ firing rate (Fig. 3A). Figure 3B shows the average cross-correlation between motoneuron cell pairs. Without Renshaw cells in the simulation (black line), this had clear oscillations at ϳ10 Hz. With the introduction of Renshaw cells, the 10 Hz periodicity in the cross- correlation was reduced and a periodicity at ϳ30 Hz appeared. Figure 3C shows the sum of the power spectra of the spiking of each motoneuron in the simulation; this is the frequency domain equivalent of the autocorrelation in Figure 3A. Peaks at 10 Hz and its harmonics were not altered by the addition of Renshaw cells. Figure 3D presents the power spectrum of the population discharge of the entire motoneuron pool. This differs from the summed power spectra of the individual cells, as correlations between neurons can now contribute. It is clear that Renshaw cells had a marked effect on the spectrum, decreasing the power at 10 Hz and increasing it at 30 Hz. Renshaw cells therefore act by changing the correlations between motoneurons. Correlations close to 10 Hz are decreased, whereas those around 30 Hz are elevated.

Phase analysis of the recurrent feedback loop Why do motoneurons synchronize at ϳ30 Hz in the simulations which include Renshaw cells? This is not a simple prod- Figure 2. A, Corticomuscular coherence for simulations without Renshaw cells (black), with uct of the Renshaw cell firing rate: on average, Renshaw cells Renshaw cells (red), and in which Renshaw cell activity was copied from a previous simulation, fired at 17 Hz in these simulations, but this comprised brief thereby opening the Renshaw cell–motoneuron feedback loop (blue). B, Power spectrum of ϳ muscle force. In B, black line indicates no Renshaw cells; red, each motoneuron receives input bursts at 60 Hz separated by pauses. One possible source of from20Renshawcells,andeachRenshawcellreceivesinputfrom50motoneurons.Simulation the 30 Hz rhythm is the delay around the recurrent feedback length throughout 4017 s. loop. To characterize the dynamics imposed by Renshaw cell feedback, we first simulated each connection in an open loop configuration. Thus one simulation contained only connec- drive to the motoneurons to maintain the required firing rate. In tions from Renshaw cells to motoneurons (Fig. 4A, blue), the the simulations which included Renshaw cells, therefore, the cor- other only had connections from motoneurons to Renshaw tical input to the motoneurons was a smaller fraction of the total cells (Fig. 4A, black). Figure 4B shows the phase of the coher- drive than when no Renshaw cells were present. Could the re- ence calculated between the total spiking of the motoneuron duced corticomuscular coherence have occurred simply because pool, and the Renshaw cell pool, for these simulations. of this “dilution” effect? The red line in Figure 4B is the sum of the phases determined To control for this possibility, we ran a further simulation in from the two open loop simulations. This indicates how mo- which the times of Renshaw cell spikes were simply copied from toneurons will influence their own firing via Renshaw cell feed- the previous simulation (Fig. 2, blue line). This ensured that the back. Two important features are evident. First, the phase crosses motoneurons received the same levels of excitatory and inhibi- ␲ radians at 10 Hz. At this frequency, oscillations are thus fed tory drive as in the simulation with recurrent inhibition, but the back to motoneurons in exact antiphase, leading to cancellation. feedback loop between Renshaw cells and motoneurons was bro- Second, the phase crosses zero at 30 Hz. The Renshaw cell recur- ken. Corticomuscular coherence was indeed reduced slightly rent feedback loop will thus tend to introduce oscillations at 30 compared with the simulation without Renshaw cells; however, Hz because of loop resonance. peaks at all frequencies were effected similarly. It is possible that A major component of the time delay introduced by the the small reduction in coherence at ϳ20 Hz is attributable to recurrent feedback loop is the rise time of the EPSPs produced dilution of the cortical input by the increased inputs required in by motoneuron spikes in the Renshaw cells. The remainder of the simulation containing Renshaw cells. However, the majority Figure 4 investigates the effects of changing this on the system 6620 • J. Neurosci., May 20, 2009 • 29(20):6616–6624 Williams and Baker • Renshaw Cells Improve Tremor dynamics. Figure 4C illustrates the three unitary EPSPs tested. The EPSP shown in red is the same as used in the simulations until this point, and best accords with known experimental data. It has a rise time of 8.0 ms. The EPSPs in green and blue have rise times of 3.0 ms and 12.6 ms respectively. Figure 4D shows the impact of changing the EPSP shape on the open-loop phase relationship between motoneuron and Renshaw cell spiking. Figure 4E adds these phase mea- surements to those for the open-loop simulations including only connections from Renshaw cells to motoneurons, thereby showing a similar plot to the red line of Figure 4B but for different EPSP shapes. In all plots there is a phase dis- continuity close to 10 Hz; the location of this is governed by the motoneuron firing rate, and is relatively insensitive to the EPSP time course. The frequency at which the phase crosses zero shifts as the EPSP duration changes. The slowest EPSP leads to a resonant frequency of 27.0 Hz, compared with 35.1 Hz for the EPSP with the fastest rise time. Figure 4F shows the effect of changing Figure 3. Effects of Renshaw cells on motoneuron firing properties. Black line indicates simulation without Renshaw cells; red the Renshaw cell dynamics on the cortico- indicates the simulation with Renshaw cells. A, Autocorrelation of motoneuron spikes, summed across the motoneuron pool. B, muscular coherence. In all cases, the size of Cross-correlation between pairs of motoneurons, summed across all possible cell pairs. Bin width 10 ms. C, Sum of power spectra the 10 Hz peak is reduced compared with of single motoneuron spike activity. D, Power spectrum of the population discharge of the motoneuron pool. the simulation without Renshaw cells (black line); the extent of this reduction is greatest for the simulation with slowly rising EPSPs. The effect on mained as Gaussian white noise. Figure 5A shows the cortico- the 20 Hz corticomuscular coherence peak is considerably altered muscular coherence calculated between the EMG and modulated by the EPSP time course. The fastest EPSP investigated reduced cortical input for simulations with (red line) and without RCs this peak, whereas the slowest augmented it. Finally, the peak (black line). Much larger coherence peaks were seen at 10 Hz and around 30 Hz was increased by the slowest EPSP, but left un- 20 Hz for both simulations when compared with unmodulated changed by the fastest EPSP. This peak was slightly shifted to cortical input (Fig. 2A), and the strength of tremor, as assessed by lower frequencies by lengthening the EPSP duration, as predicted the 10 Hz peak in the force power spectrum, was correspondingly by the loop phase analysis of Figure 4E. larger (Fig. 5B compared with Fig. 2B). However, just as for the Figure 4G shows the power spectrum of the force from these simulations with white noise input, recurrent inhibition reduced simulations; it exhibits similar effects to those seen in the corti- both corticomuscular coherence at 10 Hz and 20 Hz, and 10 Hz comuscular coherence. Figure 4H shows the power spectrum of tremor, whereas coherence was increased at 30 Hz. the Renshaw cell spike activity. This clearly demonstrates the shift Our motoneuron model included PICs, which are known to lower frequencies of the ϳ30 Hz peak as the EPSP is broad- to have an important influence on motoneuron properties. To ened. The 20 Hz peak also grows substantially for the simulation test whether PICs altered the results reported here, we ran with the slowest EPSP. The reason can be appreciated from the some simulations without PICs. This required increasing the phase display of Figure 4E: the loop phase at 20 Hz is changed level of independent input to the motoneurons to maintain from ϳ␲/2 radians to close to zero by the lengthening of the EPSP the same discharge rates as previously (independent input 9 duration, extending the range of frequencies over which resonant times greater than the cortical input, compared with 3.2 times behavior can be seen. for simulations with PICs). Figure 5C illustrates the corticomuscular coherence calculated for these simulations. Coher- Further simulations ence levels were lower than seen previously (Fig. 2A), reflect- In the simulations described until this point, the common corti- ing the lower fraction of the total motoneuron input which cal input to the motoneurons was simulated as Gaussian white came from the cortex. However, the addition of Renshaw cells noise. However, oscillations at both ϳ10 Hz and ϳ20 Hz have had a very similar effect as before: coherence was reduced at 10 been reported in the primary motor cortex during sustained con- and 20 Hz, but raised at 30 Hz. The ϳ10 Hz peak in the force tractions (Conway et al., 1995; Kilner et al., 2000; Baker et al., power spectrum (Fig. 5D) was also reduced by the addition of 2003), and it was important to determine how recurrent inhibi- Renshaw cells. The action of the recurrent inhibitory loop tion would interact with this rhythmic input to the motoneurons. does not therefore seem to be influenced by the presence or Cortical oscillations were simulated by modulating the common absence of PICs in the motoneurons. This was the case even cortical input at 10 Hz and 20 Hz; the independent input re- though the gain of the recurrent inhibitory feedback loop, Williams and Baker • Renshaw Cells Improve Tremor J. Neurosci., May 20, 2009 • 29(20):6616–6624 • 6621

wrist is also in this region. Input compo- nents around 10 Hz thus have the potential powerfully to synchronize motoneuron firing (Matthews, 1997). Muscle acts as a low-pass filter, because of the relatively slow nature of twitch tension production. However, 10 Hz is usually well within the frequency range for production of unfused contractions, meaning that rhythmic discharge of the motoneuron pool at this frequency will produce overt mechanical tremor (Elble and Randall, 1976). Previous work has suggested that Ren- shaw cells act to desynchronize motoneurons, possibly reducing physiological tremor (Adam et al., 1978; Windhorst et al., 1978); other authors suggested that recurrent inhibition could synchronize motoneurons (Windhorst, 1996). Using computational modeling, Maltenfort et al. (1998) concluded that recurrent inhibition acted to decorrelate motoneuron firing, reducing the magnitude of both positive and negative correlations between cell pairs toward zero. The amplitude of peaks in the power spectrum of motoneuron population activity was also decreased by recurrent inhibition. Importantly, in the simulations reported by Maltenfort et al. (1998), motoneuron firing rates were gen- erally above 15 Hz. In contrast, we were interested to simulate weak contractions in which many motoneurons fired at around 10 Hz, which is close to the rate at which motor units are first recruited (Milner-Brown et al., 1973). This accentu- ated the power spectral peaks of motoneuron activity around this critically important frequency, and revealed a marked reduced of synchronization at 10 Hz when Figure4. A,SchematicofconnectivityintwosimulationsruntoopenthefeedbackloopbetweenRenshawcellsandmotoneu- rons.B,CoherencephasebetweenspikesfromthepopulationofRenshawcellsandmotoneurons.Blackandbluelinescorrespond recurrent inhibition was added. to models shown in A. Red line, Sum of phases shown by black and blue lines, estimating the total loop phase. Horizontal dashed In the present work, we have shown lines mark in-phase (0 radians) and anti-phase (␲ radians); vertical dashed lines mark 10 Hz and 30 Hz frequencies. C, Different that the action of Renshaw cells is different EPSPshapestestedinsimulationsdescribedinthelinesofcorrespondingcolorintheremainderofthefigure.RedEPSPisthesame in different frequency ranges. Around the as used in simulations in previous figures. D, Coherence phase between motoneuron and Renshaw cell spikes, for the network 10 Hz frequency of physiological tremor, shown in black in A. This corresponds to the black line in B, but for the different EPSP widths shown in C. E, Total loop phase, synchronous oscillations are fed back to corresponding to the red line in B, for the different EPSP widths shown in C. F, Corticomuscular coherence. G, Force power motoneurons in anti-phase, leading to spectrum. Black line in F and G shows the results for a simulation without Renshaw cells for comparison. H, Power spectrum of cancellation. In contrast, around 30 Hz the Renshaw cell population spiking. Simulations were 4017 s long throughout. dynamics of the Renshaw cell- motoneuron loop leads to in phase, positive feedback, and a resonant augmenta- estimated as described in Materials and Methods, was only tion of this frequency. 0.058 in the simulations without PICs (compared with 0.1 Uchiyama and Windhorst (2007) also constructed a model of when PICs were included). It has been shown experimentally recurrent inhibition, and used it to investigate the effects on mo- that PICs are capable of amplifying the effect of inhibitory toneuron synchronization. They concluded that the addition of inputs (Kuo et al., 2003). Renshaw cells to the model tended to increase synchrony in the motoneuron pool. However, examination of their data shows Discussion that this effect was most marked when motoneurons fired above Frequencies close to 10 Hz pose a particular difficulty in the 20 Hz. When firing rates were close to 10 Hz, recurrent inhibition control of movement. When motoneurons are first recruited, tended to decrease motoneuron synchrony. The analysis of syn- they begin to fire around this rate (Milner-Brown et al., 1973). chronization was performed solely in the time domain, and is The monosynaptic stretch reflex arc has a tendency to oscillate hence not entirely comparable with the present work, but the around 10 Hz, and the mechanical resonant frequency of the results appear broadly compatible with our findings. 6622 • J. Neurosci., May 20, 2009 • 29(20):6616–6624 Williams and Baker • Renshaw Cells Improve Tremor

Renshaw cells may therefore form part of the neural system for filtering out ϳ10 Hz oscillations from motoneuron discharge which was hypothesized to exist by Baker et al. (2003). We found that Ren- shaw cell feedback could reduce, but not abolish, 10 Hz corticomuscular coherence. In addition, it appears that forearm muscles controlling the fingers, and intrinsic hand muscles, lack Renshaw cells in their motoneuron pools (Katz et al., 1993; Illert and Ku¨mmel, 1999). Yet corticomuscular coherence at ϳ10 Hz is also absent in these muscles (Conway et al., 1995; Baker et al., 1997, 2003; Salenius et al., 1997; Kilner et al., 2000). It is most likely therefore that multiple mechanisms exist to reduce ϳ10 Hz synchronization of motoneurons, of which Renshaw cell recurrent inhibition is just one example. The addition of Renshaw cells to a motoneuron pool will partially cancel oscillations not just at ϳ10 Hz, but also at lower frequencies (Fig. 4B). Most pathological tremors, including essential tremor, par- kinsonian tremor and cerebellar tremor have dominant frequencies below 10 Hz (Elble and Koller, 1990). It is likely therefore that the mechanism described here will also be important in these conditions. If acting normally, Renshaw cell feedback Figure 5. A, B, Results from simulations which used a cortical input modulated to contain power-spectral peaks at 10 Hz and will reduce these tremors, so that their am- 20 Hz. C, D, Results from simulations which omitted PICs from the motoneuron model. Top row (A, C) shows corticomuscular coherence; bottom row (B, D) shows force power spectrum. Black lines relate to simulations without Renshaw cells and red lines plitude will be lower than otherwise. It is to simulations in which they were included. Simulation length throughout was 2880 s. even possible that a weakening of recurrent inhibition could contribute to tremorigenesis. Whatever the source of probably the most effective anti-tremor medication in clinical pathological oscillatory drive to the motoneurons, we predict use. These observations are consistent with tremor amplitude that strengthening Renshaw cell feedback should lead to a being modulated by the relative balance between recurrent reduction of tremor amplitude. This suggests a novel avenue inhibition and recurrent excitation. of tremor therapy. Previous work has used the drug The dynamic behavior of the Renshaw cell circuit could pro- L-acetylcarnitine to alter Renshaw cell effective connectivity in vide a reason for their differential distribution across different healthy subjects (Mattei et al., 2003), but no investigations motoneuron pools. The resonant frequency of human upper have so far been performed on patients with pathological limb segments increases in a proximo-distal direction, from ϳ6 tremor. Hz at the elbow, ϳ11 Hz at the wrist to ϳ26 Hz for the index In the model presented here, we focused on recurrent inhibi- finger (Elble and Koller, 1990). Up to the wrist, therefore, me- tion, via Renshaw cells, because these are well characterized ex- chanical tremor falls within the low-frequency range within perimentally. However, there are also recurrent excitatory path- which Renshaw cells are effective at tremor cancellation. For the ways, producing positive feedback to motoneuron pools. This digits, the mechanical resonant frequency instead lies within the includes monosynaptic motoneuron-to-motoneuron connections (Cullheim et al., 1977, 1984), and also disynaptic connec- range in which the Renshaw cells actually generate oscillations tions via a recently discovered novel class of spinal interneurons (Fig. 4). Inclusion of recurrent inhibition in motoneuron pools (Machacek and Hochman, 2006). Full characterization of the supplying digit muscles would therefore be counter-productive. ϳ effects of these pathways would require their inclusion in our The generation of 30 Hz rhythms by Renshaw cell feedback model, based on the known cellular and connection properties. is a novel finding. However, in the cerebral cortex, several mod- However, it seems reasonable to suppose that they could act op- eling studies have shown that networks of inhibitory interneu- positely to Renshaw cells, enhancing 10 Hz oscillations. Interest- rons generating recurrent inhibition can lead to synchronous ingly, the disynaptic recurrent excitatory pathway is normally oscillations in the “gamma” frequency band (Wang and Buzsa´ki, suppressed, but can be unmasked by the action of noradrenaline 1996; Pauluis et al., 1999; Traub et al., 1999; Whittington et al., (Machacek and Hochman, 2006). Noradrenaline is released in 2000). A similar mechanism is likely to be operating here. By the spinal cord by projections from the locus ceruleus as part of recording from a patient with paraplegia, Norton et al. (2004) the “fear–fight–flight” response. It is well known that tremor showed that the isolated human spinal cord can generate spon- increases during anxiety. ␤-Adrenergic agonists such as salbuta- taneous rhythmic muscle discharge. The frequency of these oscil- mol enhance tremor, whereas the ␤-antagonist propranolol is lations was ϳ16 Hz, somewhat lower than the ϳ30 Hz generated Williams and Baker • Renshaw Cells Improve Tremor J. Neurosci., May 20, 2009 • 29(20):6616–6624 • 6623 by Renshaw cell feedback in our model. However, it is possible tion and afterhyperpolarization following motoneuronal discharge in the that pathological changes in spinal circuitry altered the resonant cat. 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